{"title":"Existence of a Renormalized Solution of a Quasilinear Elliptic Equation without the Sign Condition on the Lower-Order Term","authors":"L. M. Kozhevnikova","doi":"10.1134/s0012266124060041","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper considers a second-order quasilinear elliptic equation with an integrable\nright-hand side. Restrictions on the structure of the equation are stated in terms of the\ngeneralized <span>\\(N \\)</span>-function. Unlike the author’s previous papers,\nthere is no sign condition on the lower-order term of the equation. The existence of a renormalized\nsolution of the Dirichlet problem for this equation is proved in nonreflexive\nMusielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124060041","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The paper considers a second-order quasilinear elliptic equation with an integrable
right-hand side. Restrictions on the structure of the equation are stated in terms of the
generalized \(N \)-function. Unlike the author’s previous papers,
there is no sign condition on the lower-order term of the equation. The existence of a renormalized
solution of the Dirichlet problem for this equation is proved in nonreflexive
Musielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.
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